IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v118y2003i2d10.1023_a1025495204834.html
   My bibliography  Save this article

Order-Preserving Transformations and Applications

Author

Listed:
  • A. Cambini

    (University of Pisa)

  • D.T. Luc

    (University of Avignon
    Institute of Mathematics)

  • L. Martein

    (University of Pisa)

Abstract

In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a transformation preserving a given order. They are applied to derive the relationship between the efficient set of a set and its image under a linear transformation, to characterize generalized convex vector functions by using order-preserving transformations, to establish some calculus rules for the subdifferential of a convex vector function, and develop an optimality condition for a convex vector problem.

Suggested Citation

  • A. Cambini & D.T. Luc & L. Martein, 2003. "Order-Preserving Transformations and Applications," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 275-293, August.
  • Handle: RePEc:spr:joptap:v:118:y:2003:i:2:d:10.1023_a:1025495204834
    DOI: 10.1023/A:1025495204834
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1025495204834
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1023/A:1025495204834?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. The Luc, Dinh, 1995. "On the properly efficient points of nonconvex sets," European Journal of Operational Research, Elsevier, vol. 86(2), pages 332-336, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    2. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    3. A. Engau & M. M. Wiecek, 2007. "Cone Characterizations of Approximate Solutions in Real Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 499-513, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Guerraggio & D. T. Luc, 2001. "Optimality Conditions for C1,1 Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 615-629, June.
    2. A. Guerraggio & D.T. Luc, 2003. "Optimality Conditions for C 1,1 Constrained Multiobjective Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 117-129, January.
    3. Angelo Guerraggio & Dinh The Luc, 2006. "Properly Maximal Points in Product Spaces," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 305-315, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:118:y:2003:i:2:d:10.1023_a:1025495204834. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.